"How to translate FAIR?" Very simple. If it's a noun, then we mean the event. If it's an adjective, then we mean just/equal. The noun form of fair (just) is "fairness". Fair as an adjective can also mean "light" (fair hair) or "pleasant" (fair weather). Again, just look at the context and it's still simple.

The second meaning of 'fair' you mention is a type of festival that occurs during the summer and fall, mainly in rural areas. At a fair, there are games, rides, lots of food, and judging of agricultural products with the participants seeking the blue ribbon (a blue ribbon being the prize for 1st place). The type of venue that you seem to be trying to describe (e.g., trading of agricultural goods) would best be described as a 'farmers' market'. (http://en.wikipedia.org/wiki/Farmers%27_market)

I would think they are two words with two separate roots, and the same spelling. This is not uncommon because English borrows so many words over thousands of years. . Fair / Justice is really a Germanic word meaning pleasing, attractive. 'the judgement was fair / was pleasing to all'. But I think it is taken as a synonym of 'Just' which has other meanings (balance, objectivity, suitably punishing) etc. Fair / Market: I suspect it that this meaning of Fair is from french also - Fait / Faire are both forms of the Verb to do/make in French. The connection with the event is really 'A place to show the things you have made'. Sometimes this is called a Fete. (pronounced Fay't)